NDA 2019 Maths · Mathematics · Application of Derivatives · easy

The difference between the greatest and the least values of f(x)=x^3-3x^2+2 on [0,3] is

Single correct option

The difference between the greatest and the least values of

f(x)=x^3-3x^2+2

[0,3]

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Answer: (A) $4$

f'(x)=3x(x-2)

, so the critical points are

0

and

2

. Compare

f(0)=2

f(2)=-2

and

f(3)=2

at the critical points and the endpoints. The greatest value is

2

and the least is

-2

, a difference of

4

. Only checking the critical point

x=2

would hide that the maximum is

2

Original question written in the NDA 2019 Maths pattern and checked twice for the correct answer. Not an official question paper. How we write and check questions · Corrections policy · Report a mistake